Automatic packaging machines often include magazines to hold a plurality of products in stacks before the products are grouped together and packaged. However, there are a number of downsides with regard to the various magazine extraction equipment that extract products from magazines. For example, in some cases, the magazine extraction equipment requires a change of machine parts to handle products of various thicknesses. This halting of the magazine extraction equipment to switch to the appropriate machine parts results in an interruption of the automatic packaging process. As another example, some automatic packaging machines have magazine extraction equipment, which move the products at constant low speeds when handling products that are fragile or delicate. However, this slow handling of fragile or delicate products substantially limits the efficiency and throughput of the automatic packaging process.